Hybrid Approach Using Dynamic Mode Decomposition and Wavelet Scattering Transform for EEG-Based Seizure Classification

Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive-Paint Measurement Data

The World Health Organization has reported that approximately 300 million individuals suffer from the mood disorder known as MDD. Non-invasive measurement techniques have been utilized to reveal the mechanism of MDD, with rsfMRI being the predominant method. The previous functional connectivity and energy landscape studies have shown the difference in the coactivation patterns between MDD and HCs. However, these studies did not consider oscillatory temporal dynamics. In this study, the dynamic mode decomposition, a method to compute a set of coherent spatial patterns associated with the oscillation frequency and temporal decay rate, was employed to investigate the alteration of the occurrence of dynamic modes between MDD and HCs. Specifically, The BOLD signals of each subject were transformed into dynamic modes representing coherent spatial patterns and discrete-time eigenvalues to capture temporal variations using dynamic mode decomposition. All the dynamic modes were disentangled into a two-dimensional manifold using t-SNE. Density estimation and density ratio estimation were applied to the two-dimensional manifolds after the two-dimensional manifold was split based on HCs and MDD. The dynamic modes that uniquely emerged in the MDD were not observed. Instead, we have found some dynamic modes that have shown increased or reduced occurrence in MDD compared with HCs. The reduced dynamic modes were associated with the visual and saliency networks while the increased dynamic modes were associated with the default mode and sensory-motor networks. To the best of our knowledge, this study showed initial evidence of the alteration of occurrence of the dynamic modes between MDD and HCs. To deepen understanding of how the alteration of the dynamic modes emerges from the structure, it is vital to investigate the relationship between the dynamic modes, cortical thickness, and surface areas.

Analytical and computational studies of reacting flows are extremely challenging due in part to nonlinearities of the underlying system of equations and long-range coupling mediated by heat and pressure fluctuations. However, many dynamical features of the flow can be inferred through low-order models if the flow constituents (e.g., eddies or vortices) and their symmetries, as well as the interactions among constituents, are established. Modal decompositions of high-frequency, high-resolution imaging, such as measurements of species-concentration fields through planar laser-induced florescence and of velocity fields through particle-image velocimetry, are the first step in the process. A methodology is introduced for deducing the flow constituents and their dynamics following modal decomposition. Proper orthogonal (POD) and dynamic mode (DMD) decompositions of two classes of problems are performed and their strengths compared. The first problem involves a cellular state generated in a flat circular flame front through symmetry breaking. The state contains two rings of cells that rotate clockwise at different rates. Both POD and DMD can be used to deconvolve the state into the two rings. In POD the contribution of each mode to the flow is quantified using the energy. Each DMD mode can be associated with an energy as well as a unique complex growth rate. Dynamic modes with the same spatial symmetry but different growth rates are found to be combined into a single POD mode. Thus, a flow can be approximated by a smaller number of POD modes. On the other hand, DMD provides a more detailed resolution of the dynamics. Two classes of reacting flows behind symmetric bluff bodies are also analyzed. In the first, symmetric pairs of vortices are released periodically from the two ends of the bluff body. The second flow contains von Karman vortices also, with a vortex being shed from one end of the bluff body followed by a second shedding from the opposite end. The way in which DMD can be used to deconvolve the second flow into symmetric and von Karman vortices is demonstrated. The analyses performed illustrate two distinct advantages of DMD: (1) Unlike proper orthogonal modes, each dynamic mode is associated with a unique complex growth rate. By comparing DMD spectra from multiple nominally identical experiments, it is possible to identify "reproducible" modes in a flow. We also find that although most high-energy modes are reproducible, some are not common between experimental realizations; in the examples considered, energy fails to differentiate between reproducible and nonreproducible modes. Consequently, it may not be possible to differentiate reproducible and nonreproducible modes in POD. (2) Time-dependent coefficients of dynamic modes are complex. Even in noisy experimental data, the dynamics of the phase of these coefficients (but not their magnitude) are highly regular. The phase represents the angular position of a rotating ring of cells and quantifies the downstream displacement of vortices in reacting flows. Thus, it is suggested that the dynamical characterizations of complex flows are best made through the phase dynamics of reproducible DMD modes.

A rotating detonation combustor (RDC) is a novel approach to achieving pressure gain combustion. Due to the steady propagation of the detonation wave around the perimeter of the annular combustion chamber, the RDC dynamic behavior is well suited to analysis with reduced-order techniques. For flow fields with such coherent aspects, the dynamic mode decomposition (DMD) has been shown to capture well the dominant oscillatory features corresponding to stable limit-cycle or quasi-periodic behavior within its dynamic modes. Details regarding the application of the technique to RDC—such as the number of frames, the effect of subtracting the temporal mean from the processed dataset, the resulting dynamic mode shapes, and the reconstruction of the dynamics from a reduced set of dynamic modes—are analyzed and interpreted in this study. The DMD analysis is applied to two commonly observed operating conditions of rotating detonation combustion, viz., (1) a single spinning wave with weak counter-rotating waves and (2) a clapping operating mode with two counter-propagating waves at equal speed and strength. We show that care must be taken when applying DMD to RDC datasets due to the presence of standing waves (expressed as either counter-propagating azimuthal waves or longitudinal pulsations). Without accounting for these effects, the reduced-order reconstruction fails using the standard DMD approach. However, successful application of the DMD allows for the reconstruction and separation of specific wave modes, from which models of the stabilization and propagation of the primary and counter-rotating waves can be derived.

The computational simulation of fluid flows over structures still is a major research area in fluid mechanics. Because of the multiscale nature of many of the application models and consequent large amount of data, these simulations are computationally expensive, but can benefit from modern Reduced Order Models and data-driven methods. In this work, Dynamic Mode Decomposition (DMD) and its recent variation, Piecewise DMD (pDMD), are presented and compared in terms of dynamic modes extracted from the data, accuracy in reconstructing an approximation for the original dataset as a reduced order model and, most importantly, computational cost. The pDMD method is shown to be a variation of the traditional DMD that aims to improve and overcome some of the caveats of the standard version. This variation consists in decomposing the entire data into smaller datasets and applying a linear mapping independently on each one of these subsets instead of calculating a global linear fitting. Basically, it is an application of multiple DMD on small subsets instead one DMD over the whole data. Piecewise DMD is a simple and elegant idea that is based on the "divide and conquer" approach well known in the numerical analysis literature. Even though pDMD is new and should be carefully and extensively tested, it can be considered as a promising improvement over the standard DMD. The preliminary results presented in this work show how DMD can capture the dynamics and accurately reconstruct the simulation data and how pDMD can provide more accurate results when traditional DMD reaches its limitations, capture the specific dynamics of different stages of transient flows, and reduce the computational cost by 90% for a two-dimensional flow over a cylinder when compared to standard DMD. Future applications of Reduced Order Models using both DMD and pDMD include future state predictions, computationally cheap parametric simulations, and qualitative dynamic analysis of fluid flows.

Dynamic mode decomposition (DMD) has been used for experimental and numerical data analysis in fluid dynamics. Despite of its advantages, the application of the DMD methodology to investigate the natural circulation in nuclear reactors are very scarce in literature. In this paper it is applied the traditional DMD and its variation, the sparsity-promoting dynamic mode decomposition (SPDMD), for analysis of temperature and velocity fields data, generated by computational simulation of an experimental setup in reduced scale, similar to a heat removal system by natural circulation of a pool-type research reactor. Firstly the numerical data is partitioned, using a space-time correlation approach, in order to identify fundamental sequences to compute the dynamic modes. Next, the DMD and SPDMD methodologies are applied over each subsequence to obtain the dynamic modes of the temperature and velocity fields. Finally the flow fields are reconstructed and compared with the original numerical data. The conclusion is that the SPDMD performs better than DMD to represent both the temperature and velocity data.

Wavelet transforms for feature engineering in EEG data processing: An application on Schizophrenia

Predicting behavior through dynamic modes in resting-state fMRI data

The modal decomposition based on the spectra of the Koopman operator has gained much attention in various areas such as data science and optimal control, and dynamic mode decomposition (DMD) has been known as a data-driven method for this purpose. However, there is a fundamental limitation in DMD and most of its variants; these methods are based on the premise that the target system is time-invariant at least within the data at hand. In this work, we aim to compute DMD on time-varying dynamical systems. To this end, we propose a probabilistic model that has factorially switching dynamic modes. In the proposed model, which is based on probabilistic DMD, observation at each time is expressed using a subset of dynamic modes, and the activation of the dynamic modes varies over time. We present an approximate inference method using expectation propagation and demonstrate the modeling capability of the proposed method with numerical examples of temporally-local events and transient phenomena.

Dynamic mode decomposition (DMD) is a method to extract coherent modes from nonlinear dynamical systems. In this paper, we propose an extension of DMD, sparse nonnegative DMD, which generates a nonlinear and sparse modal representation of dynamics. In particular, this makes DMD more suitable for video processing. We reformulate DMD as a block-multiconvex optimization problem to impose constraints and regularizations directly on the structures of the estimated dynamic modes. We introduce the results of experiments with synthetic data and a surveillance video dataset and show that sparse nonnegative DMD can extract part-based dynamic modes from video streams.

Machine learning (ML) algorithms have been deployed in recent years as models for the analysis of complex data. The ubiquity of ML algorithms stems from their ability to learn the patterns and structures inherent in data. Additionally, they are adaptable to a wide range of data types, irrespective of size, which allows them to learn and predict the future pattern of data. In this work, dynamic mode decomposition (DMD), an ML algorithm, is deployed to analyse the pattern of gene expression data from patients with and without ovarian cancer. Ovarian cancer is one of the deadliest gynaecologic cancers worldwide. The obscure nature of the symptoms makes early detection of ovarian cancer difficult. Early diagnosis increases the chances of survival for patients. Furthermore, the modes computed from DMD are used as features and separately fed into three ML classifiers- support vector machine (SVM), decision tree (DecTr), and K- nearest neighbour (KNN) to classify the gene expression into either cancer or non-cancer categories. Multiple metrics- sensitivity, accuracy, precision, and error rate are used to assess the performance of the models, to have a balanced illustration of a model’s performance. The DecTr outperforms the other two classifiersSVM and KNN, across the metrics used in evaluating the performance of the models.

Dynamic mode decomposition (DMD) effectively captures the growth and frequency characteristics of individual modes, enabling the construction of reduced-order models for flow evolution, thereby facilitating the prediction of fluid dynamic behavior. However, DMD's predictive accuracy is inherently constrained by its inability to inherently incorporate physical principles. Therefore, for dense particulate pipe flows with complex flow mechanisms, we introduce a physics-informed dynamic mode decomposition (PIDMD) approach, which augments the purely data-driven DMD framework by incorporating the conservation of mass as a constraint. This ensures that the extracted dynamic modes adhere to known physical principles. Initially, we apply the DMD to reconstruct and predict the velocity field, comparing the results against benchmark computational fluid dynamics-discrete element method (CFD-DEM) simulations. Findings indicate that while DMD can reconstruct the flow field simulated by CFD-DEM and provide predictions of future flow states, its predictive accuracy gradually deteriorates over time. Next, we utilize both PIDMD and DMD to reconstruct and predict particle volume fraction, evaluating both models based on CFD-DEM outcomes. The results indicate that both PIDMD and DMD can predict particle aggregation toward the center, but PIDMD provides more accurate predictions regarding the size of particle aggregations and their distribution near the tube wall. Furthermore, the average prediction error for particle volume fraction using PIDMD is 6.54%, which is lower than the error of 13.49% obtained by DMD. Both qualitative and quantitative comparisons highlight the superior predictive capability of PIDMD. The methodology developed in this study provides valuable insights for high-precision predictions of particulate flows.

BackgroundImage segmentation in fluorescence microscopy is often based on spectral separation of fluorescent probes (color-based segmentation) or on significant intensity differences in individual image regions (intensity-based segmentation). These approaches fail, if dye fluorescence shows large spectral overlap with other employed probes or with strong cellular autofluorescence.ResultsHere, a novel model-free approach is presented which determines bleaching characteristics based on dynamic mode decomposition (DMD) and uses the inferred photobleaching kinetics to distinguish different probes or dye molecules from autofluorescence. DMD is a data-driven computational method for detecting and quantifying dynamic events in complex spatiotemporal data. Here, DMD is first used on synthetic image data and thereafter used to determine photobleaching characteristics of a fluorescent sterol probe, dehydroergosterol (DHE), compared to that of cellular autofluorescence in the nematode Caenorhabditis elegans. It is shown that decomposition of those dynamic modes allows for separating probe from autofluorescence without invoking a particular model for the bleaching process. In a second application, DMD of dye-specific photobleaching is used to separate two green-fluorescent dyes, an NBD-tagged sphingolipid and Alexa488-transferrin, thereby assigning them to different cellular compartments.ConclusionsData-based decomposition of dynamic modes can be employed to analyze spatially varying photobleaching of fluorescent probes in cells and tissues for spatial and temporal image segmentation, discrimination of probe from autofluorescence and image denoising. The new method should find wide application in analysis of dynamic fluorescence imaging data.

Purpose This study aims to explore the impact of surface modifications on a circular cylinder with ridges of diverse configurations. Dynamic mode decomposition (DMD) is used for flow field analysis and deep learning gated recurrent unit (GRU) framework is used to predict variations in surface pressure. Design/methodology/approach The research entails wind tunnel testing of a cylinder with ridges of different diameters and angular position in a flow field of Re = 1.01 × 105 and the surface pressure is measured by a Scanivalve pressure scanner. DMD is used to scrutinize pressure field data, elucidating significant dynamic modes and their influence on aerodynamic characteristics. The GRU model is trained with an experimental surface pressure data set, 80% for training, 15% for testing and 5% for validation phase to predict the surface pressure distribution of the model. Findings The study inferred that the ridge ratio and angular position of the ridge on a cylindrical surface significantly influence the drag coefficient (Cd), while the DMD reveals alterations in dynamic mode frequencies and amplitudes; In addition, the GRU model accurately predicts time-dependent aerodynamic characteristics, assessed through K-fold cross-validation, demonstrating superior predictive accuracy with minimal root mean squared error. Originality/value This study uses DMD for flow field analysis and the GRU model to predict the surface pressure distribution, presenting a more efficient and time-saving alternative to conventional methodologies.

Dynamic mode decomposition of forced spatially developed transitional jets